All Iglesias can do is keep putting the barrel of his bat on the middle of the baseball, as he has this spring training, and end up changing the impression of his game.

The 23-year-old Cuban defector, now in his fourth big league camp, is as deft a defensive shortstop as you’re going to find. He turns infield practice into performance art. The problem is that the Red Sox’ preferred medium of expression at shortstop isn’t leather, it’s wood.

The Red Sox are obsessed with offensive shortstops. Iglesias has hit just .135 in 35 major league games, including a .118 clip last year in 25 games.

He needed binoculars to see the Mendoza Line last season. His stint was most memorable for Bobby Valentine yanking him for a pinch hitter in the middle of an at-bat in Toronto like a scuffling stand-up comedian.

After an offseason devoted to hitting and a tutorial from Dustin Pedroia in Arizona, Iglesias’s bat has gone from producing punch lines to line drives.

Iglesias smoked two doubles in two at-bats Monday in the Red Sox’s 5-1 Grapefruit League victory over the Tampa Bay Rays. That improved his average for the spring to .333, with four of his six hits going for extra bases. By comparison, Iglesias had 14 extra-base hits in 421 at-bats between Pawtucket and Boston last season.

“To be honest with you I throw my glove away in the offseason,” said Iglesias, who doubled off Rays starter Jeremy Hellickson in the third inning and launched a Wall Ball double off Jeff Niemann in the fifth. “I don’t even take one ground ball the whole offseason, just the last two weeks throwing with my arm. But I don’t take any ground balls. I just work hard in the gym, hitting every day, sometimes two times a day. It was a really, really good offseason.”

Budding shortstop controversy? Hardly. Forget the idea that there is going to be any competition between Drew and Iglesias. You don’t pay a guy $9.5 million to be a backup. Drew is the Opening Day shortstop unless the family injury curse strikes.

“I don’t see it like a competition,” said Iglesias. “My competition is myself. That’s what I think. My competition is myself. Be a better player, and be a better teammate.”

Steve Nesius/REUTERS

Jose Iglesias’s fancy footwork and fielding aren’t in question, it’s whether he can hit in the major leagues.

Iglesias did admit that he was blindsided by the team’s decision to ink Drew, when it appeared it was Iglesias who was next up on the Sox’ ever-revolving carousel of shortstops.

“I mean I was surprised. Nobody told me anything, but you know I can’t control that,” said Iglesias. “All I can control is to be a better player, be a better teammate. Put myself in the best position possible to help this team win some ballgames.”

Pedroia advised Iglesias on how to have a more patient approach at the plate, how to set up pitchers, and how to make sure his head was in a spot where he could track the ball better. The result has been a more upright stance for Iglesias that has yielded increased confidence and results.

“He’s made some tangible adjustments with his set-up, and he has driven the ball with a little bit more authority to all fields,” said Red Sox manager John Farrell. “Anybody that has been here over a period of time has seen him defensively. There is a lot of confidence on the defensive side. We’re looking for improvement swinging the bat.”

Yes, the Red Sox like their shortstops the way the Patriots play football — full of offense and defense optional.

The wisdom of the Sox’ preoccupation with offensive production at shortstop can be questioned, especially now that Major League Baseball has drug testing with incisors instead of false teeth. Offensive shortstops were a rare breed in 2012. Only Ian Desmond of the Washington Nationals played 100 or more games at short and posted an OPS greater than .800 (.845).

Defensively, Iglesias is beyond major league ready. Passing over Iglesias could end up as yet another E-6 for the Sox.

Besides his bat, injuries have been another strike against Iglesias. Last year he missed a month in Pawtucket with a lower back strain.

Iglesias sprained his right ankle on his first double Monday, but he stayed in the game and came around to score. He was eager to report after the game that his ankle was fine, just a little tight. The lithe shortstop was more concerned about the fact he had temporarily misplaced his cellphone.

Whether the Sox will call his number as the long-term answer at shortstop is debatable. But Iglesias believes his place is with the Red Sox even if they don’t have a place for him now.

“Of course, this is a family. This is my family,” he said. “This is the organization I’ve been with for four years. This is the one that made me a better player every day. Sooner or later, my time is coming, so I just want to be ready for it.”

The reality is that Iglesias probably will never be a 20-home run hitter. He’s more Omar Vizquel than Nomar Garciaparra.

It’s not Iglesias who is going to have to change his approach. It’s the Red Sox, if he is to be their starting shortstop.